In the above description, the coupled data chunks, \(\vec{P}_1(\Delta _1)\)  and \(\vec{P}_2(\Delta _2)\)  belonging to adjacent subdomains near \(\partial \Omega _{1,2}\)  are exchanged simultaneously before the local domain solves are computed. One key advantage with such a DD scheme is that only nearest neighbor exchange of data is required, which keeps communication costs bounded as the number of subdomains \(\mathcal {N}\)  increase [1]}, [2]}, while providing opportunities to interlace recomputation of the constrained control point solution. Note that in a RAS iterative scheme, nearest neighbor exchanges can be performed compactly per dimension and direction, thereby minimizing communication costs and eliminating expensive global collectives.
